Courtesy Runners

[NealH]

I had a question from a partner I was working with last night that kinda had me thinking.

Fed rules. Player #5 courtesy runs for the pitcher at the start of the 1st inning and player #6 courtesy runs for the catcher in the same inning. The team bats around and the pitcher gets on base a second time in that inning. May player #6 courtesy run for him even though he ran for the catcher earlier in the inning? That is, is a player who is a courtesy runner for a particular player locked to that player for the whole half inning or can the courtesy runner be any qualified sub?

I told him I thought the players had to run for the same players if they are used in that inning but I couldnt find a reference that said that.